Is it permissible for my father to take all the gold he finds in the cave he discovered, or does it belong to the state?

If gold is found in a cave, bearing marks of the pre-Islamic era (Jahiliyyah) or earlier, then it is considered rikaz (a buried treasure from the time of ignorance), and it is obligatory to give one-fifth of it as charity, while the remainder belongs to them. This is based on the Prophet, peace and blessings be upon him, who said: "And in rikaz is the one-fifth." Rikaz is identified by the presence of pre-Islamic marks on it, such as the names of their kings or their images. However, if it bears an Islamic mark, then it is considered a luqatah (found lost property).